This project is centered on the mechanisms of calcium-triggered exocytosis, the ubiquitous eukaryotic process by which vesicles fuse to the plasma membrane and release their contents. The effects of calcium and the ensuing fusion depends upon protein moeties embedded into the lipid bilayer. To model this aspect of exocytisis, we consider the elastic behavior of flat lipid monolayer embedding cylindrical inclusions oriented obliquely with respect to the monolayer plane. An oblique inclusion models a fusion peptide, a part of a specialized protein capable of inducing merger of biological membranes in the course of fundamental cellular processes. Although the crucial importance of the fusion peptides for membrane merger is well established, the molecular mechanism of their action remains unknown. This analysis is aimed at revealing mechanical deformations and stresses of lipid monolayers induced by the fusion peptides, which, potentially, can destabilize the monolayer structure and enhance membrane fusion. We calculate the deformation of a monolayer embedding a single oblique inclusion and subject to a lateral tension. We analyze the membrane-mediated interactions between two inclusions, taking into account bending of the monolayer and tilt of the hydrocarbon chains with respect to the surface normal. In contrast to a straightforward prediction that the oblique inclusions should induce tilt of the lipid chains, our analysis shows that the monolayer accommodates the oblique inclusion solely by bending. We find that the interaction between two inclusions varies nonmonotonically with the interinclusion distance and decays at large separations as square of the distance, similar to the electrostatic interaction between two electric dipoles in two dimensions. This long-range interaction is predicted to dominate the other interactions previously considered in the literature. The role of cytosolic ATPases such as N-ethylmaleimide (NEM)-sensitive fusion protein (NSF) in membrane fusion is controversial. We examined the physiology and biochemistry of ATP and NSF in the cortical system of the echinoderm egg to determine if NSF is an essential factor in membrane fusion during Ca(2+)-triggered exocytosis. Neither exocytosis in vitro, nor homotypic cortical vesicle (CV) fusion required soluble proteins or nucleotides, and both occurred in the presence of non-hydrolyzable analogs of ATP. While sensitive to thiol-specific reagents, CV exocytosis is not restored by the addition of cytosolic NSF, and fusion and NSF function are differentially sensitive to thiol-specific agents. To test participation of tightly bound, non-exchangeable NSF in CV-CV fusion, we cloned the sea urchin homolog and developed a species-specific antibody for western blots and physiological analysis. This antibody was without effect on CV exocytosis or homotypic fusion, despite being functionally inhibitory. NSF is detectable in intact cortices, cortices from which CVs had been removed and isolated CVs treated with ATP-gamma-S and egg cytosol to reveal NSF binding sites. In contrast, isolated CVs, though all capable of Ca(2+)-triggered homotypic fusion, contain less than one hexamer of NSF per CV. Thus NSF is not a required component of the CV fusion machinery.